Making a hollow, 3-D pipe/duct: after joining two cubes, how can I delete the surface inside the pipe/duct to make it hollow?
First of all, I don't know if I quite understood the question correctly, but  what I got out of it tells me you have a shape like this:



And that you want to make sure that the intersection there is clean, and not screwy.

This can be accomplished with Loop-Cut-an-Slide tool. It can be accessed in edit mode by pressing Ctrl + R. when you place it on the upper cube, it looks like this:



Don't bother sliding it, just click and place it there for now. Next you're gonna want to turn on vertex snapping, it can be found on the bottom bar of your 3D view-port. Click the magnet to turn on snapping, then click the grid icon just right of it and change it to vertex, portrayed by a grey cube with two white studs on it 

once this is enabled you can select the four vertices of the loop you added and hit G + Z to Grab them down on the Z axis.

now, if you mouse over one of the vertices of your bottom cube until an orange circle appears around it, then click to finish placement.



Now all you have to do is remove those inner four vertices to get a clean cut.

If you add two loop-cuts on the bottom cube and hitS + X
 to Scale them on the X axis and then snap them to the new bottom of your top cube. Now remove doubles and your gold!



You can also do this by simply grabbing the four vertices that you don't like and G + Z to Grab them up on the Z axis until they snap with the top of the top cube.

Sorry for the super long answer. :D hope this helps, Ciao!